how to animate dripping substance
Well...

I would first assume to use blenders fluid simulation but that has restrictions. If you don't want the animation to be exported to a game or anything that requires animation exporting, don't use this method. If it is just for a still image or an internal animation, GREAT!!!

Blenders fluids have the option to change the viscosity of liquids (Thickness) so it will work perfectly for your needs. You can use either use your mesh or a child object as the inflow object. Create a domain, and bake it once you have animated everything and it should act as a fluid should :D

Your other option is only applicable if you don't want the drop to detach and fall. Sculpt your drop separate to the mesh and use soft bodies which can create a jiggling hanging effect.

Good luck with your project and I hope I helped,

BFB